Ask HN: How to do token based Authentication between an app and trusted back end?

Friends and I are trying to develop an android (and later iOS) app that interacts with our backend with resources that are protected unless a user has an account with us.

I am having trouble finding examples of how to do token based authentication with this in mind, such as OAuth 2, for the example of being able to use a closed API, and the user not having to type their password everytime a request needs to be made.